According to this model, the inflaton field is confined on the brane and only the (effective) gravitational background is modified. This reflects the fact that gravity can work in 4+1 dimensional spacetime (in the bulk) but matter fields only exist in the usual 3+1 dimensional spacetime (on the brane). As a consequence, the Friedman equation on the brane is modified as \(H^2\sim \rho +\rho ^2\) . In the high-energy limit when inflation happens, we have \(\rho \simeq V(\phi )\)  and the quadratic term is dominant, so that \(H^2\sim \rho ^2\)  during inflation. At late times such as the radiation or matter dominated eras, the quadratic term decays much faster than the linear term, so the usual Friedmann equation \(H^2\sim \rho \)  is recovered after inflation ends and sets the stage for the subsequent usual Big Bang cosmology. The modification of the Hubble rate at early times in turn affects the predictions of inflationary models. We follow a common assumption that the extra dimension does not expand nor contract; it only serves the role of modifying the effective gravitational background on the brane. Here, we study the predictions of the shaft inflaton potential (Eq. REF ) in RS2 model. The general framework of inflation in RS2 model is discussed in [1]} and references therein.
